CALCULATING ANGLES

• 6MG2.2 Use the properties of complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle.

• Objective: Understand how to find the degree measure of an angle based on other angles.

• Learning target: Answer at least 3 of the 4 angle questions correctly on the exit ticket.

• How do we calculate the missing angle in a complementary pair?

• What is x?

• Set up an equation with the two angles adding to equal 90°

• x + 29° = 90°• - 29° -29°• x = 61°

• What is y? • y + 52° = 90°• - 52° -52°• y = 38°

• How do we calculate the missing angle in a supplementary pair?

• What is m?

• Set up an equation with the two angles adding to equal 180°

• m + 108° = 180°• - 108° -108°• m = 72°

• What is v?

• What is w?

• v + 120° = 180°• - 120° -120°• v = 60°

• w + 120° = 180°• - 120° -120°• w = 60°

• This is not a coincidence! Either v or w could be used to complete a supplementary angle pair with the 120°, so they must be equal

• What are vertical angles?

• Two non-adjacent angles formed when two lines cross.

• Vertical angles have the same degree measure.

•  ∠v and   w are vertical angles∠

• Which are vertical angles?

• Only 1 and 4 form a vertical ∠ ∠angle pair because they are the only ones formed by 2 straight, intersecting lines.

• What is t? • The t and 110° are vertical angles, so t is also 110°

• What are x, y, and z?

• The 44° and x are complementary angles, so

• x + 44° = 90°• - 44° = -44°

x = 46°• x and z are vertical, so z = 46°• x and y are supplementary, so• 46 + y° = 180°• - 46° = -46°

y = 134°

Direct Station• We will use whiteboards to work on problems combining

all of the angle topics we have worked on so far: complementary, supplementary, vertical, and in triangles.

Collaborative Station• You and your partner will write mathematical sentences

using this sentence frame:

• An angle of ___ is ___________ with an angle of ___ because they __________________.

• You will have lists of possible numbers/words to fill in the blanks.

• Example: An angle of 35° is complementary with an angle of 45° because they add up to 90°.

• Write down the full sentence.

Independent Station• You will continue ST Math’s unit on volume.